EXPERIMENTS ON FREE CONVECTION HEAT
TRANSFER TO WATER IN RECTANGULAR
VERTICAL GAPS OPEN AT THE UPPER SIDE
BY B. V. KRISHNA MURTHY AND H. A. HAVEMANN
(Department of Internal Combustion Engineering, Indian Institute of Science, Bangalore-3)
Received March I, 1957
SUMMARY
Experiments have been conducted to study the effect of the gap width
on the rate of heat transfer by free convection to water in a rectangular
gap between parallel, and relatively short plates open at the upper side.
The results show that
heat transfer decreases and
is predominant whilst the
negligible.
They are presented in
of the Nusselt number on
as the width of the gap decreases the rate of
for very small widths conductive heat transfer
free convection heat transfer becomes almost
graphical form indicating the interdependence
the product of Prandtl and Garshof number.
1. INTRODUCTION
The heat transfer from vertical plates to air has been investigated by a number
of investigators. 1-4 Similarly, the heat transfer from vertical parallel plates to the
enclosed liquids between them has also been studied.°
The heat transfer to a rectangular body of water enclosed, with the exception
of the upper side which communicated with a cooled section, between short vertical
copper plates facing each other and kept at the same temperature has been studied
in the following, whereby the effect of the distance between the plates has particularly been investigated. Thus, the bottom of the gap between the plates was
kept closed and a flow pattern established characterized by two loops as shown
in Fig. 1.
2. EXPERIMENTAL ARRANGEMENT
It consisted of two wooden blocks in which the copper plates were embedded.
Behind these plates two rectangular copper boxes were fixed, which contained the
heater coils. They were connected to a variac with which the voltage could be
controlled, and thus the 'Bath temperature'. The two wooden blocks were separated along the circumference by U-type wooden pieces which determined the
distance between the plates. The top of the gap thus formed opened into a
cylindrical wooden compartment, in which two copper U-tubes were placed through
which water was passed, to remove the heat. The details are shown in Fig. I and by
83
84
B. V. KRISHNA MURTHY AND H. A. HAVEMANN
Water rev4
Thermome
Lagging
:pooling water
Heat
Copper m plot
6x1x1/8
•
Thermo- couples
br width parameter
Fie. I. Apparatus for studying heat transfer by convection from parallel
plates to fluids.
Plate IX. The copper plates measured 6" x 1" X i" (150 mm. x
25 mm. x 3 -10 mm.).
Three copper-constantan thermocouples were inserted at the back of each of these
plates as shown in Fig. 1. Into the cooling tubes also, copper-contantan thermocouples were inserted for measuring the inlet and outlet water temperatures. The
quantity of cooling water was measured which was supplied from an overhead tank
and through a control valve.
Free Convection Heat Transfer to Water in Rectangular Vertical Gaps
85
A copper-constantan thermocouple probe was introduced from the top into
the apparatus to check for any temperature gradient along the central plane between
the plates. In the case of the 1" and 4" wide gaps another thermocouple was introduced in a horizontal plane at the mid-height of the plates to measure the Bath
temperature'. The thermal e.m.f.s were measured on a precision potentiometer
with an accuracy of ± 0.01 my.
The heat removed by the cooling tubes was supplied by the top section of the
gap which in the case of the two smallest distances was 1" x in and I' x r. As
this area was very small and the investigations were confined to th: study of free
convection without change of state higher temperature differences were difficult
to realise without boiling, and thus were not attempted.
3. EXPERIMENTAL PROCEDURE
The apparatus was filled with distilled water upto the top. The heater was
switched on and the cooling water adjusted to give a steady 'Bath temperature'
which was maintained for at least an hour before readings were taken. The
desired 'Bath temperature' could be obtained by adjusting the quantity of cooling
water in the system, or by varying the voltage on the heater coils. The readings
were recorded at different times of the day and also on different days to check
their accuracy. A series of experiments was conducted with the following gap
widths:
1", r,
+" and 3".
In all the above cases except in 1" and V the non-dimensional groups N G,,
and Np r were determined, and also the heat transfer coefficient h.
4. EXPERIMENTAL RESULTS
They are expressed in terms of the following non-dimensional groups:
hD
Nusselt Number ==
NNu
Prandti Number -= k = NPr
Grashof Number = NG r =
Dapst3g4 I
it
2
where
Film coefficient of heat transfer of water Bhr- 'ft- 2 F-1.
h
D = Height of the plate ft.
k --= Thermal conductivity of water Bhr-'11-1F-1.
= Dynamic viscosity of water lbft -2 hr -1 .
b2
86
B. V. KRISHNA MURTHY AND H. A. HAVE?vIANN
C„ := Specific heat of water B/b„, -1
p
-= Density of water lb„, ft -3.
At = Difference in temperature between the plate and the centre of
bath F.
g = Acceleration due to gravity ft. hr. -2
=...-.• 1
Bath temperature (abs.) F-'
C o ji, p aid k were calculated at the mean film temperature. The variation of
the NN, with the product of the (N G , x Np r ) has been plotted in Graph I, for the
3
lO t
su
1
frill
I
41 +I111
10
4 6 810
NGr x N pr
2
4 6810
6
4
2
2
z IQ
8
6
4
2
10
9
2
It
1 Cop width
314 n
n
—sibs. Y2
t•
of
GRAPH I
three gap widths 1", is, 4".
For the if and r widths the variation of h with At
has been plotted, Graph
2. The thermocouple probes showed that the temperature
at the mid-plane between the plates was the same from bottom to top for the 1",
Free Convection Heat Transfer to Water in Rectangular Vertical Gaps
87
r, If' gap widths. In case of the it' and E widths the temperatures in the gap
centres were very much higher than those at the top chamber.
12
10
7
to
0
os
15
10
•
ye Gap width
0
20
25
30
A t °F
lf
GRAPH II
5.
DISCUSSION OF RESULTS, AND CONCLUSIONS
It is seen from the above graphs that for gap widths from 1' to i" the heat flow
is predominantly by convection, and for the other widths, i" and j", the heat
88
13. V. KRISHNA MURTHY AND H. A. HAVEMANN
transfer is mainly by conduction. The fact that the temperature at the mid-zone
between the plates was higher than that at the top chamber indicates that convection currents are not predominant any more for smaller gap widths, and that
heat transfer occurs by conduction. The variation of the Nusselt number with
kiskr x Npr) is quite pronounced for 1 width, and gradually decreases for -r gap
width. This may be due to the fact that the convection currents are more predominant in the case of larger distances between the plates.
N
The results outlined above indicate that for the given configuration maximum
heat removal occurs if the gap width is large. As the gap width decreases the
rate of heat transfer by convection decreases and heat transfer by conduction
increases. At the smallest gap width (r) heat is transferred only due to pure
conduction.
6. FUTURE WORK
A photographic study of the flow pattern in the gap fitted with transparent
side walls would yield more precise information as to where the mode of heat transfer changes.
Longer plates with wider widths and higher heat fluxes would give more information regarding the transition from one mode of heat transfer to the other, and its
dependence on parameters of the configuration considered.
7. ACKNOWLEDGEMENTS
The authors wish to thank the Department of Atomic Energy, Government
of India, under whose auspices the investigations were carried out, for permitting
the paper to be published.
Thanks are also due to the Department of Internal Combustion Engineering,
Indian Institute of Science, Bangalore, for having provideL the necessary facilities
throughout the investigations.
8. REFERENCES
1. Bosworth, R. C. L.
..
Heat Transfer Phenomena, John Wiley & Son, Inc., New York,
1952.
2.
..
Proc. Roy. Soc.,
3.
4.
Chandra, K.
McAdams, W. H.
..
Mull, W. and Reiher, H. ..
5. Yablonski, V. S. and
Yablonskaya, V. P.
Heat Transmission,
1938, A 164, 231 42.
-
McGraw Hill, New York, 1942.
-
Beiheft zum Gesundheit Ingeneiur, Reihe 1, Heft.
Dokl. Akad. Nauk. U.S.S.R.,
1948, 59, 1575-77•
28, 1930
Vol, 39, No, 2, Sec. B, P1. IX
Jour. Md. Inst. Sci.
-
•
1
1-
A
Cross section of the Apparatus with
r gap width